The Legendary Mercenary
The Dark Knight
Round 1: Random encounter with standard equipment and morals on for both. Batman is New 52 and Snake is what he was during MGS2.
Round 2: Solid Snake gets his MGS4 gear but is in his prime and Batman is Post-Crisis.
Round 3: Composite versions for both. Both get one hour of prep time.
Round 4: Both get two weeks of prep time.
Round 5: Snake gets Metal Gear Rex and Batman gets the Justice Buster or Insider suit
Round 6: Batman has his Arkham feats and Snake has his MGS1 feats.